Bala Town, Connah's Quay and Bangor City will also find out who they will face in the Europa League qualifiers.
The Albanian champions making their debut in the toughest European club competition will face a hard challenge against Sheriff, the club who has dominated Moldovan football in the past 16 years.
Aberdeen face a trip to either Kazakhstan or Bosnia in the second qualifying round of the Europa League.
RANGERS are in line for a fiery reception from AEL Limassol fans - if they land the Cypriots in the Europa League. Tirana, who have won the Albanian championship a record 24 times, are set to become the first-ever relegated Albanian team to play at a European club competition.
Celtic come into the second qualifying round and must then try to get through the third round and a play-off stage if they are to reach the Champions League group stage for the second year running.
The first leg is scheduled to take place on 29 June with the return on 6 July.
St Johnstone, who were also seeded for the draw, were drawn to play Lithuanian side Trakai and will also start their Europa League campaign at home at McDiarmid Park.